where \( b =( b_1,b_2)\)  and \(b_i \ge 0\) , \(i=1,2\) .
We will also discuss the following Ambrosio–Tortorelli approximation of the Mumford-Shah model [1]}
\(\inf _{u \in X, s \in Z} L_{MS}(u ,s ):=& \frac{\Vert u -u_0\Vert _{2}^2}{2} + \alpha \int _{\Omega } s^2 |\nabla u |^2 \mathrm {d}\sigma \\&+ \lambda \left( \varepsilon \int _{\Omega } |\nabla s |^2 \mathrm {d}\sigma + \int _{\Omega } \frac{1}{4\varepsilon } |s -1|^2 \mathrm {d}\sigma \right). \) 
